The essential characteristic of Le Sacre du printemps is that is the most dissonant and the most discordant composition that has ever been written... Never before has the system and cult of the wrong note been applied with such industry, zeal, and obstinacy. (Le Temps, June 3, 1913).
However, most music historians now agree that the riots were caused not by the music, but by the riot-happy Parisians. Concert versions within the same year were received with great enthusiasm, and the open dress rehearsal had gone without incident the day before. Nizhinsky, the choreographer, had been panned for his setting of Debussy's Jeux two weeks earlier, and the open design of the new theater and hot weather encouraged bad behavior from an atypical audience (mostly tourists).
NPR had used this story to show how passionate audiences used to be. While it is true that art music has been "ritualized" too much, demanding silent and well-behaved audiences that are socially constrained from expressing their feelings except at certain times (the end of an aria or scene, the end of a piece), the riot is not a good example of passionate feelings from the typical audience of yesteryear.
A colleague of mine (from the Women's Studies department) had used the story to suggest that Stravinsky's musical language was horribly shocking. Again, the result is basically true: Stravinsky's use of rhythm, harmony, and orchestration was an example of extremes for that time, though not a break from his previous ballets ( Firebird and Petroushka) or horribly outlandish compared to contemporary works by Debussy, Schoenberg, Webern, and Berg. But the riots were not indicative of these extremes.
The truest thing that can be said about the Parisian riots over The Rite of Spring is that it set a benchmark of succès de scandale for all avante-garde composers to strive for. This riot set Stravinsky's reputation as the leader in Modernist music, whether he caused it or not. As a recommendation to new composers who wish to make a name for themselves, make sure your audience does not like your music and has a predeliction for expressing its displeasure.